The most common and most likely answer to this crossword clue is the 9 letter word GRADUATES
I've seen this crossword clue in The Guardian
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More clues leading to the result GRADUATES
Buddy explains!
The straight part
We know that "Finishes with a Damien, Desmond or Douglas" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case finishes with a damien, desmond or douglas = graduates.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GRADUATES mean?
GRADUATES noun- A person who is recognized by a university as having completed the requirements of a degree studied at the institution.
- A person who is recognized by a high school as having completed the requirements of a course of study at the school.
- A person who is recognized as having completed any level of education.
- A graduated (marked) cup or other container, thus fit for measuring.
- To be recognized by a school or university as having completed the requirements of a degree studied at the institution.
- To be certified as having earned a degree from; to graduate from (an institution).
- To certify (a student) as having earned a degree
- To mark (something) with degrees; to divide into regular steps or intervals, as the scale of a thermometer, a scheme of punishment or rewards, etc.
- To change gradually.
- To prepare gradually; to arrange, temper, or modify by degrees or to a certain degree; to determine the degrees of.
- To bring to a certain degree of consistency, by evaporation, as a fluid.
- To taper, as the tail of certain birds.